Compact model to efficiently characterize TSV-to-transistor noise coupling in 3D ICs

A methodology is proposed to characterize through silicon via (TSV) induced noise coupling in three-dimensional (3D) integrated circuits. Different substrate biasing schemes (such as a single substrate contact versus regularly placed substrate contacts) and TSV fabrication methods (such as via-first and via-last) are considered. A compact π model is proposed to efficiently estimate the coupling noise at a victim transistor. Each admittance within the compact model is approximated with a closed-form expression consisting of logarithmic functions. The methodology is validated using the 3D transmission line matrix (TLM) method, demonstrating, on average, 4.8% error. The compact model and the closed-form expressions are utilized to better understand TSV induced noise as a function of multiple parameters such as TSV type, placement of substrate contacts, signal slew rate and voltage swing. The effect of differential TSV signaling is also investigated. Design guidelines are developed based on these results.